320 



STEEL GRAIN ELEVATORS. 



CHAP. IX. 



Now in a granular mass, the lateral pressure at any point is equal to the vertical pressure 

 times k, a constant for the particular granular material, and 



L = k-V 



Also let A/U = R (the hydraulic radius), and tan $' = /'. 

 Substituting the above in (i) we have 



dV = 

 Now let 



k-V A . 



-R^ d y 



and 



w-w-K 



Surface of \ 

 Material-* ' 



y 



L-U'dy. 



c: x 



I: 



(c) 



FIG. i. 



Integrating (3) we have 



log (w> n- V) = n-y + C 



Now if y = o, then F = o, and C = log w, and (4) reduces to" 



w - n-V 



and 



where e is the base of the Naperian system of logarithms. Solving for F we have 



V = - (i - -) 

 w 



Substituting the value of n from (2), we have 



Now if h be taken as the depth of the granular material at any point we will have 



F = j^- (i 

 Also since 



(2) 



(4) 



(5) 



(6) 



(7) 



